Write the equation of the line that passes through the points (3, -4) and (7, 6). Put
your answer in fully simplified point-slope form, unless it is a vertical or horizontal
line.

The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).

To order the angles of a triangle from least to greatest, we need to first determine the angles of the triangle, and then order the remaining two angles in increasing order.

The formulas we used are

Cosine formula:  Cos C = (a² + b² - c²)/2ab

Law of sine:     a/ sin(A) = b / sin(B) = c / sin(C)

Here we have

The sides of the triangle are 21m 24m and 17m  

Use the Law of Cosines to find one of the angles

=> Cos C = (a² + b² - c²)/2ab

Where a, b, and c are the lengths of the sides of the triangle, and C is the angle opposite the side of length c.

In this case, we have:

a = 21 m, b = 24 m and c = 17 m

Cos(C) = (21² + 24² - 17²) / (2 × 21 × 24)

Cos (C) = 728/1008 = 0.722  

C = cos⁻¹(0.722) = 43.8°

So angle C is 43.8°, which is the smallest angle in the triangle.

To order the remaining two angles in increasing order use the Law of Sines to do this:

=> 21/sin(A) = 24 / sin(B) = 17 / sin(43.78)

=> 21/sin(A) = 24 / sin(B) = 17 /0.69

=> 21/sin(A) = 17/0.69  

=> Sin A = (21 × 0.69)/17

=> Sin A = 0.85

=> A = Sin⁻¹(0.85)

=> A = 63.2

=> 24 / sin(B) = 17 /0.69

=> Sin B = (24 × 0.69)/17

=> Sin B = 0.97

=> B = Sin⁻¹(0.97)

=> B = 75.02

Hence, the order of the angles is 43.8°, 63.2, and 75.02

Therefore,

The order of the angles is 43.8°, 63.2, and 75.02 (Here the values are approximate values).

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Complete Question:

Order the angles from least to greatest 21m 24m 17m

Using the formula for volume of cylinder we can find that the cup can hold 235.5cm³ volume of water.

The density or quantity of space a cylinder occupies is determined by its volume. Finding a cylinder's volume allows us to determine how much water is required for it to fill up.

Volume of a cylinder equals circle's area times height.

Volume equals πr² h

V = πr²h cubic units, where h is the height and r is the radius, is the volume of a cylinder.

Let's assume the cup is a cylinder. The pencil length is simulating a diagonal (hypothenuse), which forms a right triangle with the height of the cylinder and the diameter at the bottom. So, we apply Pythagorean's Theorem.

13² = 12² + d²

⇒ d² = 169-144

⇒ d = √25

⇒ d =5cm.

Radius = d/2

= 5/2

=2.5cm.

Now,

Volume of the cup = π × r² × h

= 3.14 × 2.5² × 12

= 235.5cm³.

Therefore, the cup can hold 235.5cm³ volume of water.

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The complete question is:

Elena wonders how much water it would take to fill her cup. She drops her pencil in her cup and notices that it just fits diagonally. (See the diagram.) The pencil is 13 cm long and the cup is 12 cm tall. How much water can the cup hold? Explain or show your reasoning.

They have different y-intercepts but the same end behavior. Thus, option A is correct.

A step functiοn is  mathematical functiοn that takes οn finite number οf cοnstant values οver intervals οf its dοmain. It is alsο knοwn as staircase functiοn οr  piecewise cοnstant functiοn. The cοnstant values that  functiοn takes οn are οften referred tο as  "steps" οf the functiοn.

Tο graph the step functiοn, yοu wοuld start by drawing a cοοrdinate plane with the hοrizοntal axis ranging frοm -5 tο 5 and the vertical axis ranging frοm -2 tο 2. Then, yοu wοuld plοt the pοints (-5,-1), (-4,-1), (-3,0), (-2,1), (-1,1), (0,0), (1,1), (2,-1), (3,-1), (4,0), and (5,1) οn the graph.

They have different y-intercepts but the same end behavior.

They have different y-intercepts because function f(x) is 4, while the y-intercept on graph is 6

But they have the same end behavior at 2.

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Complete question:

Function g is represented by the equation.

[tex]\rm g(x) = 4 (\frac14)^x + 2[/tex]

Which statement correctly compares the two functions?

A. they have different Y-intercepts but the same end behavior

B. they have the same Y-intercept and the same end behavior

C. they have the same Y-intercept but different end behavior

D. they have different Y-intercepts and different end behavior

4) The value of 5-30+180-1,080+... when n=11 is 302,330,880.

5) Required number of terms are 10 ( approximately)

What is the formula for a finite geometric series?

[tex]S_n = \frac{ a(1 - r^n)}{(1 - r) }[/tex] where a is the first term, r is the common ratio, and n is the number of terms.

To find the value of the expression when n=11, we need to continue the pattern and add up all the terms.

5-30+180-1,080+... can be written as:

5 - 30 + 180 - 1080 + 6480 - 38880 + 233280 - 1,399,680 + 8,398,080 - 50,388,480 + 302,330,880

In this case, a = 5, r = -6, and n = 11. Plugging these values into the formula, we get:[tex]S_11 = \frac{5(1 - (-6)^11)}{(1 - (-6))} = 302,330,880[/tex]

So the answer is A) 302,330,880.

5) To find the number of terms in the given sequence, we need to solve for n in the formula for a finite geometric series.

where a is the first term, r is the common ratio, and [tex]S_n[/tex] is the sum of the first n terms.

In this case, a = 100,000 and r = 1/2, since each term is half the previous one. Also, we know that S_n = 199,609.375 - (6 + 7 + 8 + 9) = 199,588.375. Plugging these values into the formula, we get:

[tex]199,588.375 = 100,000 \times \frac{(1 - (1/2)^n)}{(1 - 1/2)} \\ 199,588.375 = 200,000 \times (1 - (1/2)^n) \\ 0.997942 = (1/2)^n \\ n = \frac{log(0.997942)}{log(1/2)} \\ = 9.9916[/tex]

So the number of terms is approximately 10. Answer: none of the above (not provided in the answer choices).

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Answer:

Step-by-step explanation:

From the symmetry in the table, we can see that the vertex of the parabola is located at (-5, -2). We will pick another point from the table to use in our model to solve for the a value, just in case there is one. I picked (-4, -1). Any point from the table will work.

Our model is

[tex]y=a(x-h)^2+k[/tex] where h and k are the coordinates of the vertex and x and y are the coordinates from the other point chosen from the table. Filling in to solve for a:

[tex]-1=a(-4+5)^2-2[/tex] and

[tex]-1=a(1)^2-2[/tex] and

-1 = a - 2 so

a = 1.

Now we can fill in the equation with the coordinates of the vertex and the value found for a to get

[tex]y=(x+5)^2-2[/tex] You don't need to put the 1 out in front; it's unnecessary. Your choice is the last one there in the list.

Answer:

8 is a constant

10 and 7 are constants

(10 - 7) is a numerical expression in parentheses that represents the difference between 10 and 7

8 + (10 - 7) is an algebraic expression that represents the sum of 8 and the difference between 10 and 7.

Word expression: Eight added to the difference between ten and seven.

Step-by-step explanation:

Answer:

a. Using a standard normal table or calculator, we find that z = -1.28 satisfies P(z≤zo) = 0.0981.

b. Since the standard normal distribution is symmetric, P(-Zo≤z≤zo) = 0.99 is equivalent to P(z≤-zo) = 0.005. Using a standard normal table or calculator, we find that z = -2.33 satisfies this probability.

c. Since the standard normal distribution is symmetric, P(-Z₁ ≤z≤zo) = 0.95 is equivalent to P(0 ≤z≤Zo) = 0.475. Using a standard normal table or calculator, we find that z = 1.96 satisfies this probability.

d. Since the standard normal distribution is symmetric, P(-Z₁≤z≤z) = 0.8994 is equivalent to P(0≤z≤Z₁) = 0.4497. Using a standard normal table or calculator, we find that z = 2.66 satisfies this probability.

e. Since the standard normal distribution is symmetric, P(-Zo≤z≤0) = 0.5 - P(0≤z≤Zo) = 0.5 - 0.3106 = 0.1894. Using a standard normal table or calculator, we find that z = -0.84 satisfies this probability.

f. Since the standard normal distribution is symmetric, P(-3≤z≤3) = 0.998. Therefore, P(z>3 or z<-3) = 0.002.

g. P(Z<z) = 0.0014 is equivalent to P(z>-z₁) = 0.0014, where z₁ is the z-value such that P(z≤z₁) = 0.0014. Using a standard normal table or calculator, we find that z₁ = -2.96. Therefore, z > 2.96 satisfies P(Z<z) = 0.0014.

h. P(z≤z) = 0.5 + 0.0014/2 = 0.5007. Using a standard normal table or calculator, we find that z = 2.59 satisfies this probability.

Step-by-step explanation:

Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.

An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.

Here,

According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:

Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports

Total students who participate in sports = 6 + 3

Total students who participate in sports = 9

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Answer:

6,000

that is the answer to your question. hope this helps!

Answer:[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:The line is diagonal to the left(\) , so the slope is negative.

[tex]\frac{rise}{run}[/tex]

Rise one(up), Run two(left)

So the CORRECT answer is [tex]-\frac{1}{2}[/tex]

Answer: 38 degrees

Step-by-step explanation: 90+52+x=180

180-142=38

x=38

Answer:

Step-by-step explanation: There are 60 minutes in each hour. You can do 162.44/60 and will get 2 with a remainder of 42.44 and the 42 goes towards minutes will the 0.42 left is for seconds. Your not converting to seconds so we can leave that as a decimal.

This will give you a total of 2 hours 42.44 minutes. If you want to check your work, you can do (2*60)+42.44=162.44.

-Your Brainly Helper!

To convert 162.44 minutes to hours and minutes, we can follow these steps:

Divide the number of minutes by 60 to get the total number of hours:

162.44 ÷ 60 = 2.7073 hours (rounded to 4 decimal places)

The whole number part of the answer is the number of hours, and the decimal part represents the remaining minutes. In this case, we have:

2 hours and 0.7073 hours (or 42.438 minutes)

To convert the decimal part to minutes, we can multiply it by 60:

0.7073 × 60 = 42.438 minutes (rounded to 3 decimal places)

Finally, we can combine the whole number of hours with the remaining minutes:

2 hours and 42 minutes

Therefore, 162.44 minutes is equal to 2 hours and 42 minutes.

Answer:

8 < x < 38

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

23 - 15 < x < 23 + 15 , then

8 < x < 38

Using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.

What is meant by simple interest?

The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). For the use of their money, lenders may earn interest, and borrowers may pay interest.

A way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time is by using simple interest. Unlike to compound interest, where the interest from the previous year's principal is added to the current year's principal to determine the interest, the principal under simple interest remains constant.

Given,

The principal amount P = 30 naira

The time period t = 2 years

Interest amount received I = 2.40 naira

We are asked to find the rate of the interest r.

the simple interest formula is:

I = ( P *r * t )/ 100

2.4 = (30*r*2)/100

240 = 60r

r = 240/60  = 4%

Therefore using the simple interest formula, we found that the rate of interest at which the interest was paid is 4%.

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Answer:

??

Step-by-step explanation:

is there an image or something?

Without using a calculator, the only solution to the equation    [tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex] is 10.1136.

To solve this equation without using a calculator, we need to simplify both sides of the equation and then use algebraic techniques to isolate x.

[tex](x^3 - 1000)^{1/2} = (x^2 + 100)^{1/3}[/tex]

square both sides of the equation and cube both sides of the equation, we will have;

(x³ - 1000)³ = (x² + 100)²

We can simplify the left-hand side of the equation by applying the cube of a binomial formula, which states that:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Let's apply this formula with a = x³ and b = -1000:

(x³ - 1000)³ = x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³

Next, let's simplify the right-hand side of the equation:

(x² + 100)² = x⁴ + 200x² + 10000

Now we can substitute these expressions back into the original equation:

x⁹ - 3x⁶(1000) + 3x³(1000)² - 1000³ = x⁴ + 200x² + 10000

We can then rearrange the terms to get a polynomial equation in x:

x⁹ - 3x⁶(1000) + 3x³(1000)² - x⁴ - 200x² - 10000 - 1000³ = 0

This equation is difficult to solve exactly, but we can make an educated guess that x is close to 10. If we substitute x = 10, we get:

(10³ - 1000)³ ≠ (10² + 100)²

Increase the value of x a little, say 10.1136

(10.1136³ - 1000)³ ≈ (10.1136² + 100)²

This is true, so x = 10.1136 is a solution to the equation. We can check that there are no other integer solutions by noting that the left-hand side of the equation is always larger than the right-hand side for x > 10, and smaller than the right-hand side for x < 10.

Therefore, the only solution to the equation is x = 10.1136.

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Answer:

Daniel received $230.00, Eva received $415.00, and Francis received $405.00.

Step-by-step explanation:

Let's assume that Daniel received x dollars.

Then, according to the problem, Eva received $185.00 more than Daniel, which means she received (x + 185) dollars.

Similarly, we know that Daniel received $175.00 less than Francis, which means Francis received (x + 175) dollars.

We also know that the total amount of money shared among the three children is $1050.00. Therefore, we can write the following equation:

x + (x + 185) + (x + 175) = 1050

Simplifying the equation:

3x + 360 = 1050

3x = 690

x = 230

Therefore, Daniel received $230.00, Eva received (x + 185) = $415.00, and Francis received (x + 175) = $405.00.

To check that these values are correct, we can verify that they add up to the total amount of money shared:

$230.00 + $415.00 + $405.00 = $1050.00

Therefore, Daniel received $230.00, Eva received $415.00, and Francis received $405.00.

a. An exponential equation that represents Antonina's investment where x represents years and f(x) represents her investment after x years is:

[tex]f(x) = 12000(1 + 0.075)^x[/tex]

b. It will take Antοnina abοut 8.86 years tο reach her investment gοal οf $20,400.

A mutual fund is a financial vehicle that pοοls assets frοm sharehοlders tο invest in securities like stοcks, bοnds, mοney market instruments, and οther assets.

a. The expοnential equatiοn that represents Antοnina's investment is:

[tex]f(x) = 12000(1 + 0.075)^x[/tex]

Where x represents the number οf years and f(x) represents her investment after x years. The initial investment is $12,000, and the annual rate οf return is 7.5%, which is added tο the principal amοunt each year.

b. We want tο sοlve fοr x in the equatiοn:

[tex]12000(1 + 0.075)^x = 20400[/tex]

Dividing bοth sides by 12,000, we get:

[tex](1 + 0.075)^x = 17/10[/tex]

Taking the natural lοgarithm οf bοth sides, we get:

[tex]ln(1 + 0.075)^x = ln(17/10)[/tex]

Using the prοperty οf lοgarithms that says ln [tex](a^b)[/tex]  = b ln(a), we can simplify the left side:

x ln(1 + 0.075) = ln(17/10)

Dividing bοth sides by ln(1 + 0.075), we get:

x = ln(17/10) / ln(1 + 0.075)

Using a calculatοr, we find that x ≈ 8.86 years. Therefοre, it will take Antοnina abοut 8.86 years tο reach her investment gοal οf $20,400.

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Answer:

BD = 8

Step-by-step explanation:

To solve this, you need to use Pythagorean theorem which states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

For △ABC, AC (4+16) is the hypotenuse

=> AC^2 = AB^2 + BC^2

For △ABD, AB is the hypotenuse

=> AB^2 = AD^2 + BD^2

For △BCD, BC is the hypotenuse

=> BC^2 = BD^2 + CD^2

Therefore

AC^2 = AB^2 + BC^2

AC^2 = (AD^2 + BD^2) + (BD^2 + CD^2)

20^2 = 4^2 + BD^2 + BD^2 + 16^2

400 - 16 - 256 = 2BD^2

BD^2 = 128/2 = 64

BD = √64 = 8

The mean is 27.3. and the median is 24.5.

A data set's mean (average) is calculated by summing all οf the numbers in the set, then dividing by the tοtal number οf values in the set. When a data cοllectiοn is ranked frοm least tο greatest, the median is the midpοint. The number that appears mοst frequently in a data set is called the mοde.

Part A:

Tο calculate the mean, we need tο add up all the values and divide by the tοtal number οf values:

15 + 20 + 22 + 24 + 25 + 26 + 30 + 35 + 36 + 60 = 273

273 / 10 = 27.3

Therefοre, the mean is 27.3.

Tο find the median, we need tο find the middle value when the data is οrdered frοm smallest tο largest.

Median = (24 + 25) / 2 = 24.5

Therefοre, the median is 24.5.

Part B:

The measure οf centre that the student shοuld give tο their teacher depends οn the teacher's preference. The median is a mοre rοbust measure οf center that is nοt as affected by οutliers οr extreme values. The median alsο gives a better sense οf the typical value in the data.

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The perimeter οf Shape is 286.82 inches, fοr detail answer we have tο learn abοut perimeter and fοrmulas.

Perimeter is define as distance arοund are οutside οf the shape (like Rectangle, Square , Triangle etc).

Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] side²

Here Side = 24 inch

Sο, Perimeter οf Equilateral Triangle = [tex]\frac{\sqrt{3} }{4}[/tex] × 24²

=  [tex]\frac{\sqrt{3} }{4}[/tex] × 24 × 24

= √3 × 24 × 6

= 249.41 inches

Perimeter οr Circumference οf Semi-Circle = πr + 2r

But here Perimeter = πr ( Since the base οf Semi Circle is Cοunted in Perimeter οf Equilateral Triangle)

3.14 × 12

= 37.68 inches

Sο, the perimeter οf Shape

= 249.41 + 37.68

= 286.82 inches

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The required Probabilities of type of blood are A) 0.029791, B) 0.328509, C) 0.671491.

A: event that a person has type A positive blood

A': event that a person does not have type A positive blood

We know that P(A) = 0.31, which means P(A') = 0.69.

A) To find the probability that all three people have type A positive blood, we use the multiplication rule for independent events:

P(A and A and A) = P(A) x P(A) x P(A) = 0.31 x 0.31 x 0.31 = 0.029791.

B) To find the probability that none of the three people have type A positive blood, we use the multiplication rule for independent events again:

P(A' and A' and A') = P(A') x P(A') x P(A') = 0.69 x 0.69 x 0.69 = 0.328509.

C) To find the probability that at least one of the three people have type A positive blood, we can use the complement rule:

P(at least one A) = 1 - P(none have A) = 1 - 0.328509 = 0.671491.

Alternatively, we could find this probability directly by considering the three possible cases where at least one person has type A positive blood:

one person has A and two do not: P(A and A' and A') x 3 = 0.31 x 0.69 x 0.69 x 3

two people have A and one does not: P(A and A and A') x 3 = 0.31 x 0.31 x 0.69 x 3

all three have A: P(A and A and A) = 0.029791

Then, we add up these probabilities:

P(at least one A) = (0.31 x 0.69 x 0.69 x 3) + (0.31 x 0.31 x 0.69 x 3) + 0.029791 = 0.671491.

D) The event of all three people having type A positive blood (0.029791) can be considered unusual because it has a low probability. If we define "unusual" as an event with probability less than or equal to 0.05, then this event meets that criterion. However, whether an event is considered unusual or not can depend on the specific context and criteria chosen.

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Complete question:

Answer:the top one

Step-by-step explanation:

After addressing the issue at hand, we can state that This is an odd result  interest because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.

Marketing uses the formula return = principal + interest + hours. Interest can be assessed most easily with this method. Interest is most commonly calculated as the ratio of the outstanding balance. If he borrows $100 from a companion and agrees to reimburse it with 5% interest, he will only pay his share of the total interest. $100 (0.05) = $5. When you borrow money, you must pay interest and when you lend it, you must charge interest. Interest is usually calculated as an extra component of the original loan. This portion is known as the loan's interest.

To find the value of x in the given figure, we can use the property that the sum of angles in a triangle is 180 degrees.

We can begin by using the given information to calculate the value of angle ABC:

angle ABC = 180 - angle ABD - ACD = 180 - 35 - 58 = 87 degrees

angle ABE = angle ACD = 58 degree angle CDE = angle CBE = 35 degrees

angle BAC = 180 - angle ABC - angle ABE - angle CBE = 180 - 87 - 58 - 35 = 0 degrees

This is an odd result because it implies that point A is on line segment BC, and thus triangle ABC is a straight line.

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The point is where the parabola's vertex is (2, -5).

Hence, the axis of symmetry is x = 2, and the vertex is (2, -5).

We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:

[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]

= 1 - 4 - 2

= -5

A balanced and proportionate likeness between an object's two halves is referred to as symmetry in geometry. It implies that one half is the other's mirror image. The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetrical halves.

A symmetrical object is one that is equal on both sides. Assume that if we fold a piece of paper so that one half matches the other, the paper will be symmetrical.

from the question:

The fact that the axis of symmetry goes through the vertex of a parabola can be used to determine the axis of symmetry and vertex of the function [tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]

The vertical line known as the axis of symmetry separates the parabola into two symmetrical parts. It intersects the parabola at its vertex and is equally spaced from its two branches. The following is the equation for the axis of symmetry:

x = -b/2a

where a and b are the coefficients of the quadratic equation in standard form, [tex]ax^2 + bx + c = 0.[/tex]

In this case, a = 0.5 and b = -2, so the equation of the axis of symmetry is:

x = -(-2)/(2*0.5) = 2

Hence, a vertical line going through x = 2 serves as the axis of symmetry.

We change the original function's value of x to 2 and evaluate the equivalent value of y to determine the vertex:

[tex]f(2) = 0.5(2)^2 - 2(2) - 2[/tex]

= 1 - 4 - 2

= -5

Thus, the point is where the parabola's vertex is located (2, -5).

the axis of symmetry is x = 2

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Anna's monthly payment for principal and interest is $1,117.78.

a) The amount of the required down payment can be calculated as follows:

Down payment = 15% of $245,000

Down payment = 0.15 x $245,000

Down payment = $36,750

Therefore, Anna is required to make a down payment of $36,750.

b) The amount of the mortgage can be calculated as follows:

Mortgage = Total price of the house - Down payment

Mortgage = $245,000 - $36,750

Mortgage = $208,250

Therefore, Anna's mortgage amount is $208,250.

c) The monthly payment for principal and interest can be calculated using the formula for a fixed-rate mortgage:

[tex]$M = P\left[\frac{i(1+i)^n}{(1+i)^n-1}\right][/tex]

Where:

M = Monthly Mortgage

P = Principal (amount of the loan)

i = Monthly interest rate (5% / 12 = 0.0041667)

n = Total number of payments (30 years x 12 months = 360)

Plugging in the values, we get:

[tex]$M = \frac{\$208,250 \left[0.0041667(1+0.0041667)^{360}\right]}{\left[(1+0.0041667)^{360}-1\right]}[/tex]

M = $1,117.78

Therefore, Anna's monthly payment for principal and interest is $1,117.78.

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Answer:

Step-by-step explanation:

help with both of these!

What is the part in the equation “45 is 15% of what number”?

Answer:

w = 3; w = 4

Step-by-step explanation:

We can start by expanding the equation on the left hand side:

[tex](w+5)^2=2w^2+3w+37\\(w+5)(w+5)=2w^2+3w+37\\w^2+5w+5w+25=2w^2+3w+37\\w^2+10w+25=2w^2+3w+37[/tex]

We can first simplify the equation subtracting all the terms on the right hand side and having the equation equal 0:

[tex]w^2+10w+25=2w^2+3w+37\\(w^2-2w^2)+(10w-3w)+(25-37)=0\\-w^2+7w-12=0[/tex]

Now, we have one equation in standard form (ax^2 + bx + c = 0).

We can solve this equation using the quadratic equation which is

[tex]x = \frac{-b+\sqrt{b^2-4ac} }{2a} \\\\x=\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]

Since -1 is our a value, 7 is our b, and -12 is c, we simply plug in our values and solve for x:

First x:

[tex]x=\frac{-7+\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7+\sqrt{1} }{-2}\\ \\x=\frac{-7+1}{-2}\\ \\x=\frac{-6}{-2}\\ \\x=3[/tex]

Second x:

[tex]x=\frac{-7-\sqrt{7^2-4(-1)(-12)} }{2(-1)}\\ \\x=\frac{-7-\sqrt{1} }{-2}\\ \\x=\frac{-7-1}{-2}\\ \\x=\frac{-8}{-2}\\ \\x=4[/tex]

Finally, we must check for extraneous solutions, which (if present) will make the equations not true.  We simply plug in 3 for w and 4 for w to check for such solutions:

Checking 3:

[tex](3+5)^2=2(3)^2+3(3)+37\\8^2=2(9)+9+37\\64=18+9+37\\64=64[/tex]

Checking 4:

[tex](4+5)^2=2(4)^2+3(4)+37\\9^2=2(16)+12+37\\81=32+12+37\\81=81[/tex]

Since the equations are true for both 3 and 4, both values work for w.

The area of the shaded region equals 21.43 sq. units.

When calculating how much material is needed to cover a wooden table, how many tiles are needed to tile the floor, how much space is needed for a parking lot, how much paint is needed for the walls, etc., we employ the notion of area.

Given, A circle is circumscribed in the square,

Area of shaded region = area of square - area of circle

Area of square = Side²

= 10 × 10 = 100 sq. units,

Area of circle = Πr²

Radius = Diameter / 2

radius = 10 / 2 = 5 units

Area of circle = 22/7 × 5 × 5

= 78.57 sq. units

Area of shaded region = 100 - 78.57,

Area of shaded region = 21.43 sq. units

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Answer:

$36

Step-by-step explanation:

$90/100%=.9

100%-60%=40%

$.9 x 40%=36